To reconcile this contradiction, we analyze the distribution of sectional curvatures for \(N\) -qubit system and find that 2-surfaces generated by Hamiltonians of size smaller than the typical size can be negatively curved. Besides the negative curvature, another basic criterion is that the typical sectional curvatures should be at the order of \(1/N^2\)  [1]}. The complexity metric we choose satisfy this requirement. It can be further shown that our choice is the only metric which satisfy the requirement up to constant corrections.
